A logarithmic amplifier (“log amp”) generates an output signal VOUT that is related to its input signal VIN by the following transfer function:VOUT=VY log(VIN/VZ)  Eq. 1where VY is the slope and VZ is the intercept as shown in idealized form in FIG. 1. Progressive compression type log amps achieve the logarithmic transfer function through the combined effect of multiple gain stages and detector cells that approximate a logarithmic law.
FIG. 2 illustrates a prior art progressive compression log amp. The log amp of FIG. 2 includes a series of cascaded gain stages 10, each of which has a relatively low linear gain up to some critical level. Above the critical level, the gain of each stage is limited to a lower level—in some cases to zero. Thus, they are also referred to as amplifier/limiter stages. A series of detector cells 12 are connected to corresponding gain stages. The outputs of the detector cells are added together to generate the log output signal. In this example, the detector cell outputs are current mode signals, so they can be added together through a simple summing connection at node N1.
FIG. 3 illustrates a prior art detector cell based on three transistors arranged as a rectifying transconductance (gm) cell. The emitter areas of the transistors are ratioed; that is, transistors Q1 and Q3 have a unit emitter area of “e”, while transistor Q2 has an emitter area of D times e. The input signal is applied across the bases of Q1 and Q3 as a differential voltage VIN. The base of Q2 is held at the midpoint of the input signal by the divider formed by input resistors RB.
The bias current IT (also referred to as a quiescent or tail current) through transistors Q1–Q3 is generated by a bias transistor QA. The level of bias current IT is determined by the voltage applied to the base of QA. An operational amplifier (op amp) 14 maintains the base of QA at the voltage VREF which is typically generated by a precision voltage reference. The same reference voltage is also applied to the bases of additional bias transistors QB, QC, etc., which provide the same bias current to the other detector cells.
The collector currents of Q1 and Q3 are summed together to form one detector output current IP, while the collector current of Q2 provides another output current IN. Either or both of the output currents may be used to generate the final logarithmic output. If IP is used as the sole output signal, the current IN may be diverted to a positive power supply VP, and the output current IP has the form shown in FIG. 4. I0 is the output current when the input signal is zero, that is, VIN=0. IL is the limit of the signal available from the detector cell when the input signal is large. Thus the maximum current swing M available at the detector output is M=IL−I0 and is related to the bias current IT and the emitter area ratio D.
FIG. 5 illustrates the detector cell output current IP in logarithmic form for several detector cells in a progressive compression log amp in which each detector cell is implemented using the IP output from the circuit of FIG. 3. The curves are shown as a function of the log input signal LOG INPUT on a logarithmic scale. The left-most curve in FIG. 5 is for the first detector cell, the next curve is for the second detector cell, etc. Each curve is offset relative to the others because the input VIN to any specific detector cell is shifted relative to the main LOG INPUT signal depending on its location along the cascade of gain stages. Thus, each curve is offset from its adjacent curve by an amount that is related to the gain A of each gain stage 10. Assuming each detector cell is fabricated using identical components on an integrated circuit, IL, I0, and M will be essentially identical for each detector cell.
FIG. 6 illustrates the final output signal obtained by summing together the output currents IP from all of the detector cells. The final output signal approximates the ideal log function shown in FIG. 1. Since each of the individual curves shown in FIG. 5 has the same maximum output swing M, the slope of the final output signal is strongly dependent on the value of M which determines the height of each of the piecewise linear approximation sections in the final output function.
Referring back to FIG. 3, if the other output current IN is used to generate the final logarithmic output, IP may be diverted to the power supply, and the IN output has an inverted shape as shown in FIG. 7. In this case, summing together the IN outputs from all of the detector cells produces a final log output signal having a negative slope as shown in FIG. 8. Note that in either case, the relative vertical position of the individual curves in FIGS. 5 and 7 generally does not affect the log slope. That is, a DC offset may be added to the curves in FIGS. 5 and 7 to shift them up or down without affecting the maximum output swing M that determines the slope of the final logarithmic output.